Noise-Induced Transitions in a Nonsmooth Producer–Grazer Model with Stoichiometric Constraints

Yuan, Sanling; Wu, Dongmei; Lan, Guijie; Wang, Hao

doi:10.1007/s11538-020-00733-y

Cited by 44 publications

(11 citation statements)

References 45 publications

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“…May 26 pointed out that in real circumstances all kinds of biological parameters for populations may suffer stochastic interferences to a greater or lesser degree. Thus, many investigators use SDEs to investigate the impact of environmental stochasticity on ecosystem, 12,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] among which Haldar et al 12 analyzed the dynamics behaviors of a modified Leslie-Gower type eco-epidemiological model with infectious disease for prey population and harvesting in the deterministic and stochastic circumstances. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of a stochastic eco‐epidemiological model with disease in predators

2022

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It is widely accepted that epidemics in biological populations and stochasticity in the environments are two important components significantly influencing the real ecosystems. To more accurately reveal developmental changes of the population dynamics and explore effective control methods for infectious disease, in this paper, we first construct a stochastic ecoepidemiological model with disease in predators, and mathematically analyze the fundamental properties of the model. Then, we establish sufficient criterion for the existence of a unique ergodic stationary distribution of the positive solution. Also, we derive sufficient conditions, respectively, for three different extinction scenarios of populations: (i) The predators go extinct, only the prey persists; (ii) both the predators and prey go extinct; and (iii) the disease is eradicated from the system, both the predators and prey persist. Finally, we perform some numerical simulations under different interferences of environment to illustrate the main theoretical results.Especially, we observe that once the disease is eradicated from the system, then the predators and prey will coexist in an oscillatory manner. Our research indicates that the environmental noises have significant impacts on the

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Section: Introductionmentioning

confidence: 99%

Dynamic analysis of a stochastic eco‐epidemiological model with disease in predators

2022

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“…Three new types of bistability comparing with [17] were found: between two positive equilibria, between one positive equilibrium and one boundary equilibria, between the limit cycle and one boundary equilibrium. For model (1.1), Yuan et al [39] accounted for the effect of environmental noises on the switch between two stochastic attractors in the bistable situation. WKL model in [34] mechanistically incorporates free nutrient in media.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a stoichiometric producer-grazer model with maturation delay

Zhang¹,

Wang²,

Niu

2022

Math Appl Sci Eng

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Ecological stoichiometry provides a multi-scale approach to study macroscopic phenomena via microscopic lens. A stoichiometric producer-grazer model with maturation delay is proposed and studied in this paper. The interaction between stoichiometry and delay is novel and leads to more interesting insights beyond classical delay-driven periodic solutions. For example, the period doubling route to chaos can occur as the minimal phosphorous:carbon ratio in producer decreases. Mathematically, we establish the conditions for the existence and stability of positive equilibria, and study the occurrence of Hopf bifurcation at positive equilibria. Analytic results show that delay can change the number and stability of positive equilibria through transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation, and it further determines the grazer's extinction. Our model with a small delay behaves like LKE model in terms of light intensity, and Rosenzweig's paradox of enrichment exists in a suitable light intensity. We plot bifurcation diagrams and show rich dynamics driven by delay, light intensity, phosphorous availability, and conversion efficiency, including that a large delay can drive the grazer to go extinct in an intermediate light intensity that is favorable for the survival of the grazer when there is no delay; a limit cycle can appear, then disappear as the delay increases; given the same initial condition, solutions with different delay values can tend to different attractors.

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“…𝐵 𝑖 (𝑡) (𝑖 = 1,2) are the standard Wiener process and 𝜎 𝑖 > 0(𝑖 = 1,2) denote the intensity of noise. It is very common to study the dynamics of the stochastic systems by constructing ellipses through stochastic sensitivity function technique [21,22]. For example, Xu et al [23,24] considered a stochastic model in which two microorganisms compete for an inhibitory growth-limiting nutrient and explored feedback control of noise-induced extinction.…”

Section: Introductionmentioning

confidence: 99%

A confidence ellipse analysis for stochastic dynamics model of Alzheimer’s disease

Gao

Liu

et al. 2022

Preprint

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The Alzheimer’s disease (AD) is a neurodegenerative disease, which is caused by the aggregation of beta-amyloid peptide (Aβ) in the patient’s brain and the disorder of Ca2+ homeostasis in neurons. Caluwé and Dupont [1] proposed a deterministic AD model to explore the effect of Ca2+ on AD. They demonstrated the positive feedback loop between Aβ and Ca2+ and the occurrence of bistability. Based on their results, we further discuss the bistable behaviors. We present two periodically feasible drug strategies to alleviate the AD and screen out more effective one. In this paper, we also formulate a stochastic AD model, analyze the existence and uniqueness of global positive solutions and establish sufficient conditions for the existence of ergodic stationary distribution. Furthermore, the confidence ellipses describing the configurational arrangement of stochastic coexistence equilibria are constructed by stochastic sensitivity function technique, and tipping threshold is estimated as well. Noise-induced stochastic switching between two coexistence equilibria is observed in bistability region. Our results provide a new idea to control noise to alleviate AD through physical therapy and drug therapy.

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Noise-Induced Transitions in a Nonsmooth Producer–Grazer Model with Stoichiometric Constraints

Cited by 44 publications

References 45 publications

Dynamic analysis of a stochastic eco‐epidemiological model with disease in predators

Dynamic analysis of a stochastic eco‐epidemiological model with disease in predators

Dynamics of a stoichiometric producer-grazer model with maturation delay

A confidence ellipse analysis for stochastic dynamics model of Alzheimer’s disease

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